Hydraulic-driven adaptable morphing active-cooling elastomer with bioinspired bicontinuous phases

The active-cooling elastomer concept, originating from vascular thermoregulation for soft biological tissue, is expected to develop an effective heat dissipation method for human skin, flexible electronics, and soft robots due to the desired interface mechanical compliance. However, its low thermal conduction and poor adaptation limit its cooling effects. Inspired by the bone structure, this work reports a simple yet versatile method of fabricating arbitrary-geometry liquid metal skeleton-based elastomer with bicontinuous Gyroid-shaped phases, exhibiting high thermal conductivity (up to 27.1 W/mK) and stretchability (strain limit >600%). Enlightened by the vasodilation principle for blood flow regulation, we also establish a hydraulic-driven conformal morphing strategy for better thermoregulation by modulating the hydraulic pressure of channels to adapt the complicated shape with large surface roughness (even a concave body). The liquid metal active-cooling elastomer, integrated with the flexible thermoelectric device, is demonstrated with various applications in the soft gripper, thermal-energy harvesting, and head thermoregulation.

W/mK for gallium).In addition, the volume fraction of LM is kept the same for the two cases (before and after stretching).It is noteworthy that the thermal conduction path length of the wave-shaped LM skeleton is the curve length of S for the segment length of L. The simplified theoretical model indicates that increasing the bending (corresponding to wave amplitude of h) of the LM skeleton would extend the thermal path and decrease the effective thermal conductivity of Kwave.Thus, the wave-shaped segment of the LM skeleton is straightened along the stretching direction, leading to a decrease in h and an increase in K wave .It is noteworthy that the upper limit value of K wave is K line (corresponding to h=0).The theoretical model is consistent with the numerical and experiment results.For example, K wave =27.1 W/mK (for Φ LM =81.4%) approaches to K line = Φ LM K LM +(1-Φ LM )K MA = 27.2W/mKunder the strain of 300% (h≈0). 1 3 ( 1) where, W was the strain energy density，c i0 (i=1,2,3) was the material constant parameter, D k (k=1,2,3) was incompressibility parameter.1 I was the first strain invariant.J was the volume ratio of deformation before to after.In this study, the LMS-ACE was set to be incompressible, that was, J=1.
Simulating the mechanical deformation and thermal conductivity of LMSE.The mechanical deformations and heat transfer were effectively obtained by modules of the static structure and Fluent.The LMSE was modeled by calculating the total deformation and thermal conductivity while considering the mechanical and thermal properties of the materials used in the model (as summarized in Supplementary Table 1 and Supplementary Table 3).The LMSE consisted of both the LM and elastomer, forming a cubic model.The material properties of this composite were equivalent to those of LMS-ACE, which can be considered as a homogeneous hyperelastic material.It is important to note that the volume of the LM remained constant throughout.The specific boundary conditions were applied for deformation simulation: 1) The displacement stretch was constrained along two surfaces in one direction while allowing free deformation in other directions; 2) Rotation displacement on four surfaces (excluding stretched surfaces) was constrained to zero.Post-processing allowed the deformation values for both LM and elastomer models to be obtained.In order to determine the thermal conductivity of LMSE, heat transfer processes within the models were simulated.A fixed temperature difference (100 k) between front/back surfaces along X, Y, Z directions was set while isolating other surfaces.Subsequently, CFD-post processing enabled calculation of total heat Q on heat source surface using Fourier's law equation to obtain equivalent thermal conductivity.
where, ΔT is the absolute temperature difference between the two ends of the intercepted model, Q is the heat flux of the heat source surface, A is the heat source surface area of the model, d is the length of the intercepted model.

Supplementary Fig. 3 .
The demonstration and photograph of the tight structure thoroughly prevent LM from perfusing into the support part.(A) FDM-printed ABS model with computer-aided design.(B, C) The internal cross-section of the designed model.(D) Optical photograph of the FDM-printed ABS mold.(E) Optical photograph of the mold with vacuuming infiltration LM. (F, G) Optical photographs of complicated LMS geometry with hollow structure after the ABS full dissolution with the inner dense support structure.(H, I) Optical photographs of complicated LMS geometry with obstructed structure after the ABS full dissolution with the inner support structure with gaps.Supplementary Fig. 5. Coating layer thickness of LMS.(A) Impacts of the dipping number on the coating layer thickness for the coating materials of pure silicone or LMEE (80 wt% LM).(B) LMS (with a thickness of 0.4 mm) is coated with silicone (a thickness of 0. 3mm) to obtain a thickness of 1 mm, which reduces to 0.3 mm (the coating thickness of about 0.09 mm) at a strain of 300 %.Values in A represent the mean with error bars (n = 3; independent samples).Supplementary Fig. 8. Mechanical characteristics of LMSE.(A) Illustrations of ABS infilling pattern of FDM printing, including types of Grid, Honeycomb, Cubic, Concentric.(B) SEM of LMS micro-structures for different infilling patterns and optical images of LMSE with different LMS patterns under the strain of 300%.(C) Optical photographs of the different topological micro-structure of LMSE stretching to 600% strain.Grid, Φ LM =42.9%;Honeycomb, Φ LM =59.3%;Cubic, Φ LM =48.1%;Concentric, Φ LM =44.5%.Supplementary Fig. 11.The simplified theoretical model of stretching-enhanced thermal conductivity in the stretching direction for LMSE.The wave-shaped segment of the Gyoid-type LM skeleton is straightened along the stretching direction.For the segment length of L and cross-section area of A (including the LM skeleton cross-section area of A LM , indicating the volume fraction of LM with Φ LM =A LM /A), the relation between the thermal flux (Q) and the temperature difference (ΔT) can be used to estimate the effective thermal conductivity (K) of LMSE.To simplify the theoretical analysis, we assume that the thermal conduction of LMSE with a large content of the LM (Φ LM >40%) is mainly determined by the LM skeleton due to the low heat conductivity of the silicone matrix (K MA =0.2 W/mK) compared with LM (K LM =33.4

Table 3 .
Thermal parameters used in the finite element simulations